Dr. Fowler  CCM Functions

Vocabulary Iteration – A repetitive process Recursive Equation – shows how to calculate the next term from the current Sequence – List where each item is based on previous terms using a pattern Domain – the set of all X values Range – the set of all Y values Independent Variable – a variable like X whose values DO NOT depend on another Dependent Variable – a variable like Y whose values DO depend on another

How would you use your calculator to solve 52? Input Output Press: 5 x2 25 The number you entered is the input number (or x-value on a graph). The result is the output number (or y-value on a graph). The x2 key illustrates the idea of a function.

Graph Equation Table of values A set of ordered pairs Mapping A function is a relation that gives a single output number for every valid input number. A relation is a rule that produces one or more output numbers for every valid input number. There are many ways to represent relations: Graph Equation Table of values A set of ordered pairs Mapping These are all ways of showing a relationship between two variables.

A function is a rule that gives a single output number for every valid input number. To help remember & understand the definition: Think of your input number, usually your x-coordinate, as a letter. Think of your output number, usually your y-coordinate, as a mailbox.

A function is a rule that gives a single output number for every valid input number. Input number Output number Can you have one letter going to two different mail boxes? Not a FUNCTION

A function is a rule that gives a single output number for every valid input number. Input number Output number Can you have two different letters going to one mail box?

Are these relations or functions? & Relation x y 1 2 3 4 x y 5 6 7 5 6 7

Are these relations or functions? Not a Function but a Relation x y x y 5 6 1 7 1 6 1 2 5 6 7

Are these relations or functions? x y Not a function But a relation 5 6 8 11 1 2 3 x y 5 6 11 8

These all represent the SAME function! In words: Double the number and add 3 As an equation: y = 2x + 3 These all represent the SAME function! As a table of values: x y -2 -1 -1 1 0 3 1 5 As a set of ordered pairs: (-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)

Functional Notation An equation that is a function may be expressed using functional notation. The notation f(x) (read “f of (x)”) represents the variable y.

Functional Notation Cont’d Example: y = 2x + 6 can be written as f(x) = 2x + 6. Given the equation y = 2x + 6, evaluate when x = 3. y = 2(3) + 6 y = 12

Functional Notation Con’t For the function f(x) = 2x + 6, the notation f(3) means that the variable x is replaced with the value of 3. f(x) = 2x + 6 f(3) = 2(3) + 6 f(3) = 12

Evaluating Functions Given f(x) = 4x + 8, find each: f(2) 2. f(a +1) = 4(2) + 8 = 16 = 4(a + 1) + 8 = 4a + 4 + 8 = 4a + 12 = 4(-4a) + 8 = -16a+ 8

Evaluating More Functions If f(x) = 3x  1, and g(x) = 5x + 3, find each: 1. f(2) + g(3) = [3(2) -1] + [5(3) + 3] = 6 - 1 + 15 + 3 = 23 2. f(4) - g(-2) = [3(4) - 1] - [5(-2) + 3] = 11 - (-7) = 18 3. 3f(1) + 2g(2) = 3[3(1) - 1] + 2[5(2) + 3] = 6 + 26 = 32

Excellent Job !!! Well Done